Question

for a certain class, the following data table compares how many students play an instrument or a sport. what is the probability that a student chosen randomly from the class plays a sport or an instrument?
plays an instrument
does not play an instrument
plays a sport
2
3
does not play a sport
15
7

Explanation:

Step1: Calculate total number of students

Add all values in the table: \(2 + 3+15 + 7=27\)

Step2: Calculate number of students who play a sport or an instrument

Use the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Here, \(n(\text{plays sport})=2 + 3=5\), \(n(\text{plays instrument})=2+15 = 17\), \(n(\text{plays both}) = 2\). So \(n(\text{plays sport or instrument})=5+17 - 2=20\)

Step3: Calculate the probability

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P=\frac{20}{27}\)

Answer:

\(\frac{20}{27}\)